Lifting Topological Codes: Three-Dimensional Subsystem Codes from Two-Dimensional Anyon Models
Abstract
Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise. The physical origins of this single-shot property remain elusive, in part due to the scarcity of known models. To address this challenge, we provide a systematic construction of a class of topological subsystem codes in three dimensions built from Abelian quantum double models in one fewer dimension. Our construction not only generalizes the recently introduced subsystem toric code [Kubica and Vasmer, Nat. Commun. 13, 6272 (2022)] but also provides a new perspective on several aspects of the original model, including the origin of the Gauss law for gauge flux, and boundary conditions for the code family. We then numerically study the performance of the first few codes in this class against phenomenological noise to verify their single-shot property. Lastly, we discuss Hamiltonians naturally associated with these codes, and argue that they may be gapless.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Acknowledgement
J.B. was funded by the Research Foundation—Flanders via Grant No. G087918N and postdoctoral fellowship 12E9223N. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Industry Canada and by the Province of Ontario through the Ministry of Colleges and Universities. This project (EOS 40007526) has received funding from the FWO and F.R.S.-FNRS under the Excellence of Science (EOS) programme. We would like to thank Hussain Anwar, Lander Burgelman, Elijah Durso-Sabina, Pei Jiang, and Sam Roberts for helpful discussions. We thank Lander Burgelman for comments on an earlier draft.
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Additional details
- Research Foundation - Flanders
- G087918N
- Research Foundation - Flanders
- 12E9223N
- Innovation, Science and Economic Development Canada
- Government of Ontario
- Ministry of Colleges and Universities
- Fund for Scientific Research
- EOS 40007526
- Caltech groups
- AWS Center for Quantum Computing